Transparent media such as glass and air are transparent because light propagates through them without being scattered or absorbed. In contrast, opaque materials prevent transmission of light by absorption or scattering. Highly scattering random media such as biological tissue, turbid water, white paint, and egg shells are opaque because they contain randomly arranged particles, which cause light to scatter in many directions. This scattering effect becomes more pronounced as the thickness of the highly scattering random medium increases, and less and less normally incident light is transmitted through the medium. Scattering thus severely curtails the usefulness of optical techniques for sensing and imaging in highly scattering random media.
Previous work in the field has shown the existence of eigen-wavefronts that dramatically increase the transmission of electromagnetic signals in highly scattering random media (viz., wavefronts with transmission coefficients close to 1). By measuring the scattering of light that has passed through a highly scattering random medium, such eigen-wavefronts can be determined. For a given highly scattering random medium, an optimal wavefront that maximizes transmission through the medium can be produced from the eigen-wavefronts. Existing coordinate descent methods for determining such optimal wavefronts suffer from two main problems that limit the use of such methods in many applications. First, existing methods require measurement within or on the far side of the medium from the source of the signal. Second, existing methods converge to an optimal wavefront slowly. Existing coordinate descent methods maximize the measured intensity of each mode of a transmitted wavefront while holding the amplitudes and phases of all other modes constant. The process must then be repeated for each of M modes, requiring on the order of M measurements. Other existing methods use multiple frequencies to find the optimal phases simultaneously, but these other methods still require measurement through the medium and have only been shown to work for small numbers of modes.